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Chapter 13: Q12. (page 706)

Solve triangle ABC using the given measurements if a=14,C=90and鈭�b=13. Round measure of sides to the nearest tenth and angles to nearest degree.

Short Answer

Expert verified

The solution for triangle ABC isc=19.1,A=47and鈭�B=43掳.

Step by step solution

01

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as a=14,C=90and鈭�b=13.

02

Step 2. Calculation.

In triangle ABC, a=14,C=90and鈭�b=13.

Now, in right triangle ABC,

c2=a2+b2鈥塯颈惫别蝉,c2=142+132c=142+132c=19.1

Now by trigonometric ratios,

cosB=accosB=1419.1B=cos鈭�11419.1B=43掳cosB=accosB=1419.1B=cos鈭�11419.1B=43掳

Now, C=90and鈭�B=43掳, therefore by angle sum property A=47掳.

03

Step 3. Conclusion.

Thesolution for triangle ABC, is a=16.6,A=47and鈭�B=43掳.

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a. sin30=鈭�12

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